Modern Computer Algebra

Author : Joachim von zur Gathen,Jürgen Gerhard
Publisher : Cambridge University Press
Page : 811 pages
File Size : 47,9 Mb
Release : 2013-04-25
Category : Computers
ISBN : 9781107245259

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Modern Computer Algebra by Joachim von zur Gathen,Jürgen Gerhard Pdf

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Author : Joachim von zur Gathen. Jürgen Gerhard
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 2013
Category : Electronic
ISBN : 1107241871

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Modern Computer Algebra, Third Edition by Joachim von zur Gathen. Jürgen Gerhard Pdf

Author : Joachim von zur Gathen,Jürgen Gerhard
Publisher : Cambridge University Press
Page : 811 pages
File Size : 53,5 Mb
Release : 2013-04-25
Category : Computers
ISBN : 9781107039032

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Modern Computer Algebra by Joachim von zur Gathen,Jürgen Gerhard Pdf

Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.

Author : Keith O. Geddes,Stephen R. Czapor,George Labahn
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 46,5 Mb
Release : 2007-06-30
Category : Computers
ISBN : 9780585332475

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Algorithms for Computer Algebra by Keith O. Geddes,Stephen R. Czapor,George Labahn Pdf

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Author : Richard P. Brent,Paul Zimmermann
Publisher : Cambridge University Press
Page : 236 pages
File Size : 53,5 Mb
Release : 2010-11-25
Category : Computers
ISBN : 0521194695

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Modern Computer Arithmetic by Richard P. Brent,Paul Zimmermann Pdf

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.

Author : Edmund A. Lamagna
Publisher : CRC Press
Page : 350 pages
File Size : 45,5 Mb
Release : 2019-01-15
Category : Mathematics
ISBN : 9781351605830

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Computer Algebra by Edmund A. Lamagna Pdf

The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems

Author : Joel S. Cohen
Publisher : CRC Press
Page : 472 pages
File Size : 54,8 Mb
Release : 2003-01-03
Category : Computers
ISBN : 9781439863701

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Computer Algebra and Symbolic Computation by Joel S. Cohen Pdf

Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polyno

Author : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642558269

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Computer Algebra Handbook by Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning Pdf

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Author : Joel S. Cohen
Publisher : CRC Press
Page : 323 pages
File Size : 49,5 Mb
Release : 2002-07-19
Category : Computers
ISBN : 9781439863695

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Computer Algebra and Symbolic Computation by Joel S. Cohen Pdf

This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and

Author : J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 51,8 Mb
Release : 2007-12-10
Category : Mathematics
ISBN : 9783540737254

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Rational Algebraic Curves by J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz Pdf

The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Author : Friedrich W Hehl,Roland A. Puntigam,Hanns Ruder
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642957321

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Relativity and Scientific Computing by Friedrich W Hehl,Roland A. Puntigam,Hanns Ruder Pdf

For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

Author : Wolfram Koepf
Publisher : Springer Nature
Page : 384 pages
File Size : 49,9 Mb
Release : 2021-08-12
Category : Mathematics
ISBN : 9783030780173

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Computer Algebra by Wolfram Koepf Pdf

This textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration. Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.

Author : Sándor Dominich
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 49,5 Mb
Release : 2008-04-03
Category : Computers
ISBN : 9783540776598

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The Modern Algebra of Information Retrieval by Sándor Dominich Pdf

This book takes a unique approach to information retrieval by laying down the foundations for a modern algebra of information retrieval based on lattice theory. All major retrieval methods developed so far are described in detail, along with Web retrieval algorithms, and the author shows that they all can be treated elegantly in a unified formal way, using lattice theory as the one basic concept. The book’s presentation is characterized by an engineering-like approach.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 44,9 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175

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A Book of Abstract Algebra by Charles C Pinter Pdf

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Author : Nadiya Gubareni
Publisher : CRC Press
Page : 363 pages
File Size : 54,5 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9781000209532

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Introduction to Modern Algebra and Its Applications by Nadiya Gubareni Pdf

The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.